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Exponential Synchronization Rate of Kuramoto Oscillators in the Presence of a Pacemaker

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2 Author(s)
Yongqiang Wang ; Inst. for Collaborative Biotechnol., Univ. of California, Santa Barbara, Santa Barbara, CA, USA ; Doyle, F.J.

The exponential synchronization rate is addressed for Kuramoto oscillators in the presence of a pacemaker. When natural frequencies are identical, we prove that synchronization can be ensured even when the phases are not constrained in an open half-circle, which improves the existing results in the literature. We derive a lower bound on the exponential synchronization rate, which is proven to be an increasing function of pacemaker strength, but may be an increasing or decreasing function of local coupling strength. A similar conclusion is obtained for phase locking when the natural frequencies are non-identical. An approach to trapping phase differences in an arbitrary interval is also given, which ensures synchronization in the sense that synchronization error can be reduced to an arbitrary level.

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Automatic Control, IEEE Transactions on  (Volume:58 ,  Issue: 4 )